Algebra 2

The sum of the reciprocals of two consecutive even integers is 9/40. this can be represented by the equation shown. (1/x)+(1/x+2)=9/40
Use the rational equation to determine the integers. Please help!! I have no idea what to do:(

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  1. the common denominator is ... x (x + 2) * 40 = 40 x^2 + 80 x

    multiplying ... 40 x + 80 + 40 x = 9 x^2 + 18 x

    9 x^2 - 62 x - 80 = 0

    use the quadratic formula to find x

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  2. So the answer is just 8? or is it 8 and 10? I need two even integers. This is confusing:(

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  3. Always define your variables.

    let the smaller even integer be x
    let the larger even integer be x+2
    1/x + 1/(x+2) = 9/40
    follow R_scott's steps to get
    9x^2 - 62x - 80 = 0
    which factors to:
    (x - 8)(9x + 10) = 0
    x = 9 or x = -10/9, but we want an integer, so x = 8

    by my definition, the smaller is 8 and the larger is 10

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  4. I’m still confused

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  5. Yeah, me too Steve.

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